Question

01) Determine o periodo, a imagem e construa o grafico de cada uma das funções abaixo:
a) f(x) -3sen(x)
b) f(x) = cos(4x)
c) f(x) = 1- sen(3x)
d) f(x) = -cos(x)
e) f(x)=2cos (3/×)-3
f)f(x) =-1+2sen(0,5x)

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)~\underline{\rm gr\acute afico~representado~no~anexo~1}\\\sf p=\dfrac{2\pi}{1}=2\pi~~Im=[-3,3]\\\\\tt b)~\underline{\rm gr\acute afico~representado~no~anexo~2}\\\\\sf p=\dfrac{2\pi\div2}{4\div2}=\dfrac{\pi}{2}~~ Im=[-1,1]\\\tt c)~\underline{\rm gr\acute afico~representado~no~anexo~3}\\\sf P=\dfrac{2\pi}{3}~~Im[0,2]\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)~\underline{\rm gr\acute afico~representado~no~anexo~4}\\\sf p=\dfrac{2\pi}{1}=2\pi~~Im=[-1,1]\\\tt e)~\underline{\rm gr\acute afico~representado~no~anexo~5}\\\sf p=\dfrac{2\pi}{\frac{1}{3}}=2\pi\cdot3=6\pi~~~Im=[-1,-5]\end{array}}$

$\Large\boxed{\begin{array}{l}\tt f)\\\sf p=\dfrac{2\pi}{\frac{1}{2}}=4\pi~~Im[-3,1]\end{array}}$